- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

New massless spectra from cosmic string cusps

Amelia Drew1,2,3,4,* and Ivan Rybak5,6,†

  • *Contact author: adrew@ictp.it
  • †Contact author: irybak@ibs.re.kr
PDF

Phys. Rev. D 114, L081302 – Published 5 October, 2026

DOI: https://doi.org/10.1103/4p3h-4kzb

Abstract

In the standard picture of cosmic strings, cusps are generic features of Nambu-Goto loops where the string momentarily reaches the speed of light. They have a characteristic sharp profile, following y∼x2/3 in the (x,y) plane, and produce strong gravitational-wave (GW) bursts with waveform κ˜(ω)∝ω−4/3, making them key targets for GW searches. However, under certain conditions, this generic picture can differ. We identify novel cusp solutions with different, including smooth, shapes and compute their massless GW and axion spectra. We derive a general expression for all possible Nambu-Goto cusp spectra with the asymptotic form κ˜(ω)∝ω−n/(2n−1)ω−m/(2m−1) where n, m≥2. We calculate the effect on the waveform of realistic corrections to the Nambu-Goto description, such as those from backreaction and finite string width, which introduce a high-frequency cutoff.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (57)

  1. T. W. B. Kibble, J. Phys. A 9, 1387 (1976).
  2. T. W. B. Kibble, NATO Sci. Ser. C 549, 7 (2000).
  3. M. B. Hindmarsh and T. W. B. Kibble, Rep. Prog. Phys. 58, 477 (1995).
  4. A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, England, 2000).
  5. T. Damour and A. Vilenkin, Phys. Rev. D 64, 064008 (2001).
  6. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. D 97, 102002 (2018).
  7. R. Abbott et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Phys. Rev. Lett. 126, 241102 (2021).
  8. A. Afzal et al. (NANOGrav Collaboration), Astrophys. J. Lett. 951, L11 (2023); 971, L27(E) (2024).
  9. H. Quelquejay Leclere et al. (European Pulsar Timing Array, EPTA Collaborations), Phys. Rev. D 108, 123527 (2023).
  10. M. Gorghetto, E. Hardy, and G. Villadoro, J. High Energy Phys. 07 (2018) 151.
  11. M. Gorghetto, E. Hardy, and G. Villadoro, SciPost Phys. 10, 050 (2021).
  12. M. Buschmann, J. W. Foster, A. Hook, A. Peterson, D. E. Willcox, W. Zhang, and B. R. Safdi, Nat. Commun. 13, 1049 (2022).
  13. H. Kim, J. Park, and M. Son, J. High Energy Phys. 07 (2024) 150.
  14. K. Saikawa, J. Redondo, A. Vaquero, and M. Kaltschmidt, J. Cosmol. Astropart. Phys. 10 (2024) 043.
  15. J. Correia, M. Hindmarsh, J. Lizarraga, A. Lopez-Eiguren, K. Rummukainen, and J. Urrestilla, Phys. Rev. D 111, 063532 (2025).
  16. J. Correia, M. Hindmarsh, J. Lizarraga, A. Lopez-Eiguren, K. Rummukainen, and J. Urrestilla, arXiv:2512.13653.
  17. R. L. Davis and E. P. S. Shellard, Phys. Lett. B 214, 219 (1988).
  18. C. J. Burden, Phys. Lett. 164B, 277 (1985).
  19. D. Garfinkle and T. Vachaspati, Phys. Rev. D 36, 2229 (1987).
  20. R. A. Battye and E. P. S. Shellard, Nucl. Phys. B423, 260 (1994).
  21. A. Vilenkin and T. Vachaspati, Phys. Rev. D 35, 1138 (1987).
  22. T. Damour and A. Vilenkin, Phys. Rev. Lett. 85, 3761 (2000).
  23. B. P. Abbott et al. (LIGO Scientific and Virgo Collaborations), Phys. Rev. D 100, 024017 (2019).
  24. Vachaspati and T. Vachaspati, Phys. Lett. B 238, 41 (1990).
  25. K. D. Olum and J. J. Blanco-Pillado, Phys. Rev. D 60, 023503 (1999).
  26. A. Drew, T. Kinowski, and E. P. S. Shellard, Phys. Rev. D 110, 043513 (2024).
  27. B. Zwiebach, A First Course in String Theory (Cambridge University Press, Cambridge, England, 2006).
  28. T. W. B. Kibble and N. Turok, Phys. Lett. 116B, 141 (1982).
  29. N. Turok, Nucl. Phys. B242, 520 (1984).
  30. D. Garfinkle and T. Vachaspati, Phys. Rev. D 42, 1960 (1990).
  31. J. J. Blanco-Pillado and K. D. Olum, Phys. Rev. D 59, 063508 (1999); 103, 029902(E) (2021).
  32. A. Drew and E. P. S. Shellard, Phys. Rev. D 105, 063517 (2022).
  33. A. Drew and E. P. S. Shellard, Phys. Rev. D 107, 043507 (2023).
  34. M. R. Anderson, F. Bonjour, R. Gregory, and J. Stewart, Phys. Rev. D 56, 8014 (1997).
  35. I. Y. Rybak, Eur. Phys. J. C 85, 1121 (2025).
  36. T. Vachaspati and A. Vilenkin, Phys. Rev. D 31, 3052 (1985).
  37. T. Damour and A. Vilenkin, Phys. Rev. D 71, 063510 (2005).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/4p3h-4kzb contains the derivation of a waveform in the local wave zone of a non-periodic source [Eq. (22)], and details of the gauge transformation that removes the Xc,±(1)μ term in the exponent of I±μ for cusps [Eq. (28)].
  39. M. Sakellariadou, Phys. Rev. D 42, 354 (1990); 43, 4150(E) (1991).
  40. P. Binetruy, A. Bohe, T. Hertog, and D. A. Steer, Phys. Rev. D 80, 123510 (2009).
  41. M. Sakellariadou, Phys. Rev. D 44, 3767 (1991).
  42. T. Damour, B. R. Iyer, and B. S. Sathyaprakash, Phys. Rev. D 62, 084036 (2000).
  43. M. Dine, N. Fernandez, A. Ghalsasi, and H. H. Patel, J. Cosmol. Astropart. Phys. 11 (2020) 041.
  44. I. Y. Rybak and L. Sousa, J. Cosmol. Astropart. Phys. 11 (2022) 024.
  45. C. Hagmann and P. Sikivie, Nucl. Phys. B363, 247 (1991).
  46. J. N. Benabou, M. Buschmann, S. Kumar, Y. Park, and B. R. Safdi, Phys. Rev. D 109, 055005 (2024).
  47. R. A. Battye and E. P. S. Shellard, Phys. Rev. D 53, 1811 (1996).
  48. A. Buonanno and T. Damour, Phys. Rev. D 60, 023517 (1999).
  49. P. Auclair, K. Leyde, and D. A. Steer, J. Cosmol. Astropart. Phys. 04 (2021) 005.
  50. J. J. Blanco-Pillado, D. Jiménez-Aguilar, J. Lizarraga, A. Lopez-Eiguren, K. D. Olum, A. Urio, and J. Urrestilla, J. Cosmol. Astropart. Phys. 05 (2023) 035.
  51. J. M. Wachter, K. D. Olum, J. J. Blanco-Pillado, V. R. Gade, and K. Sivakumar, Phys. Rev. D 113, 043521 (2026).
  52. J. M. Wachter, K. D. Olum, and J. J. Blanco-Pillado, Phys. Rev. D 113, 083533 (2026).
  53. J. C. Aurrekoetxea, J. J. Blanco-Pillado, A. García Martín-Caro, and J. M. Queiruga, arXiv:2603.05243.
  54. E. J. Copeland, R. C. Myers, and J. Polchinski, J. High Energy Phys. 06 (2004) 013.
  55. E. O’Callaghan, S. Chadburn, G. Geshnizjani, R. Gregory, and I. Zavala, J. Cosmol. Astropart. Phys. 09 (2010) 013.
  56. W. E. East and J. Huang, J. High Energy Phys. 12 (2022) 089.
  57. P. Auclair et al., J. Cosmol. Astropart. Phys. 04 (2019) 034.

Outline

Information

Phys. Rev. D 114, L081302– Published 5 October, 2026
  • Received 12 March 2026
  • Accepted 25 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation